Question

7. If the length of one leg of a right triangle is three times the length of the other and the hypotenuse is 20, find the length

of the shorter leg (round your answer to the nearest tenth).

Answer 1

6.3 units

Explanation:

We let x be the length of the shorter leg.

This implies that the length of other leg in terms of x is 3x , as shown in the image.

Using Pythagorean Theorem, we can find the value of x.

This implies that,

`{x}^(2) + {(3x)}^(2) ={20}^(2)`

`\implies{x}^(2) +9{x}^(2) =400`

`\implies10{x}^(2) =400`

We divide through by 10

`\implies \frac{10 {x}^(2)}{10} = (400)/(10)`

`\implies{x}^(2)=40`

Taking positive square root of both sides,we obtain;

`x = √(40)`

`\implies x = 6.3 units`